code stringlengths 3 6.57k |
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d(P) |
A.derivation(x) |
A.derivation(y) |
A.derivation(z) |
A.derivation([2, z, x^2+y^2]) |
M.category() |
Dx.bracket(Dy) |
d.bracket(Dx) |
A.fraction_field() |
A.derivation_module(B) |
A.hom([QQ(0) |
QQ(1) |
QQ(2) |
A.derivation_module(ev) |
M.gens() |
M.gen(0) |
M.gen(1) |
M.gen(2) |
Dx(f) |
at (0,1,2) |
Dy(f) |
at (0,1,2) |
Dz(f) |
at (0,1,2) |
B.hom([B(y) |
B(z) |
B(x) |
B.derivation_module(twist=theta) |
Field (twisting morphism: x |--> y, y |--> z, z |--> x) |
M.gen() |
d(x) |
d(y) |
d(z) |
d(x + y + z) |
Caruso (2018-09) |
Copyright (C) |
RingDerivationModule(Module, UniqueRepresentation) |
__init__(self, domain, codomain, twist=None) |
A.derivation_module() |
TestSuite(M) |
run() |
GF(5) |
GF(25) |
GF(7) |
RingDerivationModule(R5, R25) |
RingDerivationModule(R5, R5^2) |
Traceback (most recent call last) |
RingDerivationModule(R5, R7) |
Traceback (most recent call last) |
R5.hom([R5.gen() |
RingDerivationModule(R5, R25, twist=theta) |
RingDerivationModule(R7, R7, twist=theta) |
Traceback (most recent call last) |
Rings() |
Commutative() |
TypeError("the domain must be a commutative ring") |
Rings() |
Commutative() |
codomain.has_coerce_map_from(domain) |
codomain.coerce_map_from(domain) |
elif (isinstance(codomain,Map) |
codomain.category_for() |
is_subcategory(Rings() |
codomain.domain() |
has_coerce_map_from(domain) |
codomain.domain() |
codomain.domain() |
coerce_map_from(domain) |
defining_morphism.codomain() |
not (isinstance(twist, Map) |
twist.category_for() |
is_subcategory(Rings() |
TypeError("the twisting homomorphism must be an homomorphism of rings") |
twist.domain() |
twist.domain() |
coerce_map_from(domain) |
twist.codomain() |
codomain.coerce_map_from(twist.codomain() |
domain.gens() |
twist(g) |
defining_morphism(g) |
except (AttributeError, NotImplementedError) |
rings (with non free modules of derivations) |
domain.is_field() |
elif (domain is ZZ or domain in NumberFields() |
FiniteFields() |
isinstance(domain, IntegerModRing_generic) |
or (isinstance(domain, pAdicGeneric) |
and (domain.is_field() |
domain.absolute_e() |
elif (isinstance(domain, (PolynomialRing_general, MPolynomialRing_base, PowerSeriesRing_generic, LaurentSeriesRing) |
or (isinstance(domain, FractionField_generic) |
isinstance(domain.ring() |
RingDerivationModule(domain.base_ring() |
self._base_derivation.gens() |
domain.gens() |
tuple(self._base_derivation.basis() |
domain.gens() |
tuple(self._base_derivation.dual_basis() |
domain.gens() |
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